Over 40 years ago, Phil Anderson wrote, “It is only slightly overstat- ing the case to say that physics is the study of symmetry” (1). Moreover, he argued, some of the most interesting and fundamental physics emerges
from the study of broken symmetry. For example, isotropic atoms, when interacting
through isotropic forces, can coalesce to form
a plainly not-isotropic crystal. On page 295
of this issue, Harter et al. (2) present results
that prove Anderson’s point by identifying
a subtle symmetry change in the correlated
metal Cd2Re2O7 that may point the way to a
new phase of matter—a type of quantum liquid crystal.

Cd2Re2O7 undergoes a structural phasetransition at 200 K (see the figure) (3). In thehigh-temperature cubic phase, a subset of theoxygen atoms sit at the vertices of octahedra,and the rhenium atoms sit at the vertices oftetrahedra. Below the transition temperature,half of the oxygen octahedra expand along acommon axis, whereas the other half con-tract. Importantly, although the cubic struc-ture preserves inversion symmetry, P: (x, y,z) → (−x, −y, −z), the low-temperature struc-ture breaks it as this operation exchangeselongated octahedra with contracted ones.

But the electronic properties also change
below the transition point, and these have
remained a lingering mystery. Cd2Re2O7 is a
relatively poor metal above the 200 K transition, with an electrical resistivity that falls
gradually with decreasing temperature. Below the transition, the temperature-dependent resistivity nosedives and ultimately
reaches a value more than an order of magnitude smaller than if the transition had not occurred. Similarly dramatic effects were seen
in other measurements that are sensitive to
the conduction electrons. Structural probes
showed that the transition involves atomic
displacements so tiny that they are difficult
to observe without specialized x-ray or neutron diffraction facilities. How could such
small structural changes cause such large
changes in the electronic properties?

In 2015, Fu (4) predicted that the electronsin certain types of metals should be suscep-tible to a new class of phase transitions thatwould also break inversion symmetry. The200 K transition in Cd2Re2O7 was singledout as a prime candidate. If correct, the elec-tronic behavior would be the cause, not theeffect, of the structural transition.

Whereas atoms occupy distinct positions
in a crystal, it is better to think of the electrons in a metal in terms of quantum states
with distinct linear momentum p, in which
momentum coordinates are (px, py, pz). The
set of all occupied states in this space is
bounded by the Fermi surface. Electrons also
have an intrinsic magnetic moment, or spin,
which can point up or down along a particular direction. The most symmetric state
has all momentum states within a spherical
Fermi surface occupied by pairs of up- and
down-spin electrons (see the figure).

The transition that Fu envisioned for
Cd2Re2O7 is similar to what happens in metallic iron at its magnetic transition temperature, but with different symmetry properties.
In its magnetic state, the Fermi surface of iron
splits into two, one for spin-up and the other
for spin-down, to produce a state with an
overall magnetic moment. This state breaks
time-reversal symmetry, T: t → −t, reversing
the direction of both linear momentum and
spin and preserving inversion, which just
reverses momentum. In the inversion-break-ing transition proposed for Cd2Re2O7, spin-orbit coupling causes the spin direction to
vary over the two Fermi surfaces so that the

At room temperature, the structure
looks the same if it is inverted around
a rhenium atom.

Inversion symmetry is lost below the
transition temperature, as adjacent
octahedra distort.

Structural symmetry

The room-temperature Cd2Re2O7 crystal
structure has a high degree of symmetry.

In the Re2O6 subunit, the rhenium atoms
form a corner-sharing tetrahedral network,
with oxygen octahedra centered on each
tetrahedron.

Unstable electrons
Measurements indicate
that the electrons in Cd2Re2O7
also change symmetry below
the transition and induce the
structural change. Related
changes occur in magnetic
metals. In the new phase,
electrons occupy spin-momentum states that break
inversion.

0 K
293 K

200 K

(x, y, z) (–x, –y, –z)

(x, y, z) (–x, –y, –z)

FerromagnetNew phaseT

P

= Oxygen

= Rhenium

Electrons drive structural change
New evidence suggests that a structural phase transition
in Cd2Re2O7 is caused by a novel electronic instability.